The value of`Delta _(f) G^(Ө)` for formation of `Cr_(2) O_(3)` is `– 540 kJmol^(−1) ` and that of `Al_(2) O_(3)` is `– 827 kJmol^(−1)`. Is the reduction of `Cr_(2) O_(3)` possible with `Al` ?

Explanation

The two equations are:
`(4)/(3)Al_(s)+O_(2(g))toAl_2O_(3(s)),triangle_(f)G^(ɵ)=-827kJmol^-1` ..(i)
`(4)/(3)Cr_(s)+O_(2(g))to(2)/(3)Cr_2O_3,triangle_(f)G^(ɵ)=-540kJmol^-1` ..(ii)
Subtracting Eq. (ii) from Eq. (i) we get
`(4)/(3)Al_(s)+(2)/(3)Cr_2O_3to(2)/(3)Al_2O_3`
`triangle_(f)G^(ɵ)=-287kJmol^-1`
Since t`triangle_(f)G^(ɵ)` of the combined redox reaction is -ve, hence reduction of `Cr_2O_3` by Al is possible.